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Flow Characteristics of Curved Rotor Stator Systems Using Large Eddy Simulation

  • Mohammad Darvish Damavandi
  • Amir NejatEmail author
Article

Abstract

In this paper, the new idea of application of a curved rotor disk in rotor stator systems is presented and analyzed by using the large eddy simulation technique. The geometry of the examined rotor-stator system consists of a stationary flat disk (stator), a rotating curved disk (rotor) and a stationary enclosing cylinder (shroud). A hole in the center of stator allows the flow to enter the cavity, and the clearance between the shroud and rotor enables the flow to exit the cavity. Employing elliptical bumps with different geometrical parameters on the rotor disk (creating a curvature on the rotor), the rotating curved disk is parametrized. Three cavity cases (one with a flat rotor disk, another with the maximum outflow total pressure, and the third with the highest mass flow rate) are selected for LES analysis and more detailed investigation of flow and turbulence structures. The Favre-filtered governing equations for LES analysis of compressible turbulent flows are solved for all three cases. Radial and circumferential flow velocities as well as shear and normal Reynolds stresses in different cavity regions are studied. The flow in a rotor-stator cavity is simultaneously affected by the inlet flow, rotor rotation, and the bump on rotor disk. Creating a bump on rotor disk causes increase of both the radial pressure gradient and the mass flow rate of fluid that enters the rotor-stator cavity.

Keywords

Curved rotor disk Elliptical bump LES Reynolds stresses Outflow total pressure Boundary layer 

Nomenclature

a

Semi-minor axis of elliptical bump (m)

b

Semi-major axis of elliptical bump (m)

Cw

Non-dimensional mass flow rate

e

Total energy (J)

G

Gap ratio

Gc

Shroud clearance ratio

h

Distance between the center of elliptical bump and rotation axis (m)

K

Entrainment coefficient

l

Inlet radius (m)

M

Moment applied on rotor (N m)

Ma

Mach number

\( \dot{m} \)

Mass flow rate (kg s−1)

∆P

Total pressure difference between inlet and outlet (bar)

p 

Static pressure (bar)

Pr

Prandtl number

qj

Heat flux vector (W m−2)

R

Disk radius (m)

Reθ

Rotational Reynolds number

Rij

Reynolds stress tensor with i, j = (r,θ, z)

r, θ, z

Cylindrical coordinate

S

Distance between disks (m)

Sc

Clearance between rotor and shroud (m)

\( {\overset{\sim }{S}}_{ij} \)

Resolved strain rate tensor

Tt 

Total temperature (K)

T

Static temperature (K)

t

Time (s)

ui

Cartesian velocity components (m s−1)

Vr, Vθ, Vz

Radial, circumferential and axial velocity components (m s−1)

\( {v}_r^{\prime },{v}_{\theta}^{\prime },{v}_z^{\prime } \)

Fluctuation of radial, circumferential and axial velocity components (m s−1)

xi i-th

Cartesian coordinates (m)

Abbreviations

DNS

Direct numerical simulation

FD

Finite difference

ILES

Implicit large eddy simulation

LES

Large eddy simulation

RANS

Reynolds averaged Navier-Stokes

RMS

Root mean square

SVV

Spectral vanishing viscosity

SGS

Sub-grid scale

Greek Symbols

α

Turbulent stress on the scalar level

β

Sub-grid scale pressure-velocity

γ

Specific heat ratio

δij

Kronecker delta

ε

Rate of dissipation

η

Kolomogorov length scale

κ 

Sub-grid scale turbulent dissipation rate

λT

Turbulent flow parameter

μ

Dynamic viscosity (N s m−2)

ν

Kinematic viscosity (s−1 m2)

π

Sub-grid scale pressure-dilatation

ρ 

Fluid density (kg m−3)

σij 

Viscous stress tensor

τij 

Sub-grid scale stress tensor

Ω

Rotational speed (rpm)

Subscripts

b 

Basic cavity configuration (flat rotor)

m 

Modified cavity configuration (rotor with elliptical bump)

Other Operators

\( \overline{.} \)

(Filtering)

\( \overset{\sim }{.} \)

Favre filtering

\( \widehat{.} \)

Indicates that the quantity is based on filtered variables

\( \overset{=}{.} \)

Shows the unit surface normal

Notes

Funding

The result of this article is a part of ongoing PhD research thesis and there was no funding for this research.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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